Proximal Point Algorithm with Euclidean Distance on the Stiefel Manifold

Bayesian inference on the Stiefel manifold

The Stiefel manifold Vp,d is the space of all d×p orthonormal matrices, and includes the d−1 hypersphere and the space of all orthogonal matrices as special cases. It is often desirable to parametrically or nonparametrically estimate the distribution of variables taking values on this manifold. Unfortunately, the intractable normalizing constant in the likelihood makes Bayesian inference challe...

The proximal distance algorithm

The MM principle is a device for creating optimization algorithms satisfying the ascent or descent property. The current survey emphasizes the role of the MM principle in nonlinear programming. For smooth functions, one can construct an adaptive interior point method based on scaled Bregman barriers. This algorithm does not follow the central path. For convex programming subject to nonsmooth co...

A Matrix-Algebraic Algorithm for the Riemannian Logarithm on the Stiefel Manifold under the Canonical Metric

Note on the convex hull of the Stiefel manifold ∗ Kyle

In this note, we characterize the convex hull of the Stiefel manifold and we find its strong convexity parameter. We also introduce the notion of roundness of a set and show that the Stiefel manifold is round.

Quadratic programs over the Stiefel manifold

We characterize the optimal solution of a quadratic program over the Stiefel manifold with an objective function in trace formulation. The result is applied to relaxations of HQAP and MTLS. Finally, we show that strong duality holds for the Lagrangian dual, provided some redundant constraints are added to the primal program. © 2005 Elsevier B.V. All rights reserved.